Lived in Versailles for 3 years. The Cloaked provides a lot of good information.
Getting around Paris on Trains or the RER/Metro isn't expensive, and they are frequent and generally ontime.
The weather in mid-March is usually pretty mild. Expect temperatures well above freezing (8-14 celcius/44-55 farenheit or so). Expect a few days of rain.
Make sure you head on out to Versailles, the Chateau is pretty awesome (bonus points if you find it without having to ask the locals, I lost count of how many times I was stopped and asked for direction by Americans speaking >really bad< french. For reference, I can butcher the French language better than most Americans can, even having lived there for years.
Montparnasse Tower was pretty cool, and definately something to visit. I only really did the Paris sightseeing thing once, and that was in mid-February - when the weather was atrocious (-5 celcius, snow, near blizzard conditions at times) - and the Tower provided a welcome alternative to the Eiffel tower. I'd only really recommend visiting the Tower if you can get there really early, before the queues start to hit. I certainly wouldn't recommend queueing for hours there.
The Louvre is highly recommended, and I'd recommend stopping by and taking in the sights at Notre Dame.
Take a walk down the Champs-Élysées. One of the most famous streets in the world. Witness, and be amazed at the feat that is the Arc de Triomphe, and stand there wondering how thousands of people don't die on that road each year. :p
Make sure you book (they speak English if you don't feel up for trying to book a table in French), and stop by the Black Dog bar and restaurant (
http://www.blackdog-bar.com/). When I lived there, they served the best Steak in Paris. The Chef has since left, but the food there is still exceptional - according to my friends who still live in Paris.
There's tons of little side cafes and restaurants that you can stop by, and you can find food at any time of the day or night. Out drinking all night and fancy a steak at 7am? No problem.
